Can the sides of a triangle have lengths 1, 9, and 9? Choices: (A)yes (B)no

Check Triangle Inequality Theorem: To determine if these can be the sides of a triangle, we need to check the triangle inequality theorem. The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Check 1 + 9 > 9: Check if 1 + 9 > 9. Calculation: 1 + 9 = 10, and 10 > 9, so this part is true. Check 1 + 9 > 9: Check if 1 + 9 > 9. Calculation: 1 + 9 = 10, and 10 > 9, so this part is also true. Check 9 + 9 > 1: Check if 9 + 9 > 1. Calculation: 9 + 9 = 18, and 18 > 1, so this part is true too. Confirm Triangle Formation: Since all conditions of the triangle inequality theorem are met, the sides 1, 9, and 9 can indeed form a triangle.

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Can the sides of a triangle have lengths $1$ , $9$ , and $9$ ? $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

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Q. Can the sides of a triangle have lengths

1

9

, and

9

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Check Triangle Inequality Theorem: To determine if these can be the sides of a triangle, we need to check the triangle inequality theorem. The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Check 1 + 9 > 9: Check if 1 + 9 > 9. Calculation: $1 + 9 = 10$ , and 10 > 9, so this part is true.
Check 1 + 9 > 9: Check if 1 + 9 > 9. Calculation: $1 + 9 = 10$ , and 10 > 9, so this part is also true.
Check 9 + 9 > 1: Check if 9 + 9 > 1. Calculation: $9 + 9 = 18$ , and 18 > 1, so this part is true too.
Confirm Triangle Formation: Since all conditions of the triangle inequality theorem are met, the sides $1$ , $9$ , and $9$ can indeed form a triangle.